Design of a PIV objective maximizing the image signal-to-noise ratio

PIV (particle image velocimetry) systems use a camera to take snapshots of particles carried by a fluid at some precise instants. Signal processing methods are then used to compute the flow velocity field. In this paper, the design of the camera objective (optics) is addressed. The optimization is done in order to maximize the signal-to-noise ratio of in-focus particles. Four different kinds of noise are considered: photon shot noise, thermal and read noise, background glow shot noise, and noise made by the other particles. A semi-empirical model for the lens aberrations of a two-doublet objective is first addressed, since further, it is shown that lens aberrations (low f-value $f_{\#}$) should be used instead of the Fraunhofer diffraction (high f-value) for the fitting of the particle image size with the pixel size. Other important conclusions of the paper include the expression of optimum values for the magnification M, for the exposure period $\tau$ and for the pixel size $\xi$.